The $350 iPhone SE was Apple's last 4-inch iPhone. It was one of the best "budget" phones on the market, but all that changed at Apple's last keynote, where the iPhone SE (along with the iPhone X) were wiped from Apple's iPhone lineup.
Today, the iPhone SE is near impossible to find. However, Amazon currently has an Unlocked iPhone SE 32GB in Space Gray for $249.99. That's $100 cheaper than the phone's regular price. (The iPhone SE in Rose Gold is also available at the same $249.99 price).
The iPhone SE sports a 4-inch Retina display, Apple's A9 chip with M9 coprocessor, 4K video recording at 30fps, 1.2 megapixel FaceTime HD camera, and a 12 megapixel rear camera. The iPhone SE supports Apple Pay and it has a Touch ID sensor. It's also capable of running iOS 12. However, that's as modern as your phone will get.
Nevertheless, if it's a budget iPhone you want — this might be your last chance to snag a sub-$300 iPhone.